Electronic musical instruments fall into two broad types. The older of these two types consists of those instruments which use various types of oscillators or clock sources as the ultimate source of a musical waveform. In instruments of this type the spectral characteristics (harmonic content, etc.) of the waveform obtained is inherently limited by the electrical characteristics of the source and of various filtration circuits which are used to modify the waveform downstream.
Another type of instrument, developed in more recent years, is not so limited. This type generates a musical waveform the amplitude of which, at each one of a plurality of sample points, is dictated by an amplitude instruction stored at a selected address in a digital memory. Thus, the waveshape is not simply a function of one or more electronic circuit parameters. This technique, which will be referred to hereinafter as "digital" waveform generation, allows considerably more flexibility in generating musical waveforms, because it permits any succession of amplitude values which can be specified by a series of numerical instructions stored in a memory.
But it is also subject to the disadvantage of excessive demand for memory capacity under certain circumstances. If the waveform to be generated is of long duration, up to as much as thirty seconds, then the required number of amplitude instructions is too great to be stored economically, and without special techniques the memory cost becomes prohibitive.
Increasing the spacing between amplitude sampling points would effectively reduce the total number of amplitude instructions to be stored, but that is an unpalatable alternative because resolution is thereby lowered to the point where audio quality is perceptibly impaired.
At least one prior art reference, U.S. Pat. No. 3,763,364 of Deutsch and Ashby, has disclosed a technique of recirculatory memory addressing as a means of reducing the memory capacity requirement in a digital waveform generator. When the last in a series of waveform amplitude instructions has been retrieved from memory, the same series of amplitude instructions is simply re-used over and over again, as long as the generated waveform lasts.
Instead of scanning the memory addresses in the same direction on each iteration, however, Deutsch et al reverse the numerical direction of address scan at the conclusion of each complete sweep, and scan back in the opposite numerical direction. The result is a series of back-and-forth address sweeps: forward, rearward, forward, rearward, and so on as long as the waveform lasts. In this context "forward" means an initial numerical direction of memory scan (normally, but not necessarily, the direction of increasing numerical address); while "rearward" means the return direction (normally, but not necessarily, the direction of decreasing numerical address). The advantage of such direction reversal is that it eliminates sudden discontinuities in the waveform amplitude at the end of each scan, which would produce audible distortion of the music.
But Deutsch et al only show how to use the direction reversal approach for producing a periodic waveform. The Deutsch instrument uses a stored sequence of waveform amplitude instructions one quarter cycle in length. The first forward address scan thus produces a first quarter wavelength of the output waveform, and the first rearward return scan produces a second quarter wavelength. The third quarter cycle is produced by a repeat forward scan, and thus is an exact repetition of the first quarter cycle. The fourth quarter cycle is produced by a repeat rearward scan, and thus is an exact repetition of the second quarter cycle. The waveform continues to repeat in that fashion (all odd quarter cycles alike, all even quarter cycles alike) for as long as the waveform lasts. Thus, the waveform of Deutsch et al is inherently periodic.
In certain circumstances it is necessary or desirable to produce a prolonged aperiodic waveform. For example, a clash of cymbals or some other percussive sound decaying over many seconds at an exponential rate cannot be effectively mimicked by a periodic waveform. Yet the duration of the sound is so great as to call for use of the recirculating scan technique in order to keep the memory capacity requirements within acceptable bounds. One of the objectives of this invention, therefore, is to adapt the recirculating scan technique to the generation of aperiodic waveforms such as exponentially decaying percussives.
The recirculating scan technique, as employed for example in Deutsch et al is also subject to another limitation. The recycling of the address scan at a steady rate (twice per cycle in Deutsch) produces flutter at the recycling frequency which is audibly detectable in the musical output. In a prolonged musical sound such audible flutter is objectionable.
Finally, the strictly periodic recycling technique of Deutsch et al. precludes any change in the spectral characteristics (for example, a decrease in higher harmonic content) of the generated waveform. Such a change over the duration of a prolonged percussive decay waveform would make the resulting sound seem more natural.